Ferrofluid Modeling

Ferrofluid Modeling

Overview of Research

The goal of this research was to study the behavior of electrically conductive ferrofluids in the presence of electric and magnetic fields. This work modeled an isolated single-peak normal field instability.

What are Ferrofluids?

Ferrofluids, also referred to as magnetic fluids, are superparamagnetic liquids. In the absence of any magnetic field, these fluids behave like any other fluid. When in presence of a magnetic field, they become strongly magnetized. The magnetization of these fluids is a consequence of nanoscale magnetic particles suspended within the fluid which respond to an externally applied field.

The first patent for a ferrofluid was filed by Stephan Papell in 1963.1 In his patent, Papell created a kerosene based fluid. He envisioned the magnetic properties of this fluid could be harnessed to draw the ferrofluid (i.e. propellant) towards the turbo pump inlet for a rocket engine in a weightless environment. Papell’s vision was never brought to fruition.

(Left) Magnetic nanoparticles are coated with a surfactant, which serves to suspend the particles in the carrier fluid. (Center & Right) Particles are randomly orientated in the fluid in an absence of a magnetic field. In the presence of the field, particles align with the local field direction.

These fluids demonstrate several documented instabilities. Possibly the most eminent of these instabilities is the normal-field instability.2 This results when these fluids are subjected to a magnetic field, a series of valleys and peaks form, which is also often referred to as the Rosensweig instability. The peaks will form a stable geometry that will minimize the gravitational, magnetic, and surface energies.

Figure 3.4: Perturbated ferrofluid interface resulting from a uniform magnetic field. Interface will remain flat along z0 until a critical field is applied. Diagram adapted from (Rosensweig 1997).2
Linear array of ferrofluid peaks.

Researchers within the Isp Lab at Michigan Tech demonstrated that electrospray emission can be achieved via the combined electro-magnetic instability. When a strong electric field is applied to a fluid meniscus, the fluid will stretch. For a sufficiently strong electric field, the fluid can deform into a sharp cone and a spray of fluid will emerge from the fluid apex. This process is known as electrospray. The demonstration that electrospray can be achieved from a combined electro-magnetic instability motivated this work.

Experiment

Small droplets of ferrofluid were placed within the uniform magnetic field generated by a Helmholtz coil. The plate on which the ferrofluid rested was biased with respect to a parallel grounded electrode to generate an electric field. Droplets were then silhouetted imaged and imaged.

Modeling Approach

Modeling was performed using COMSOL Multiphysics using the two-phase flow: moving mesh technique to model the interface. This method precisely tracks the fluid interface, which is critical for accurate estimation of the magnetic and electric stresses. Magnetic and electric stresses were added by coupling the Maxwell stress tensor with the fluid stress tensor along the droplet interface.

Results

The results of this work were published in Physics of Fluids in June of 2017 in an article titled: Ionic liquid ferrofluid interface deformation and spray onset under electric and magnetic stresses

Sources

  1. P. S. Stephen, (Google Patents, 1965).
  2. R. E. Rosensweig, Ferrohydrodynamics. (Courier Dover Publications, 1997).